Transcript 土壩有效應力動態分析與離心機實驗

Effective-stress Based Dynamic Analysis
and
Centrifuge Simulation of Earth Dam
Yii-Wen Pan1 Hui-Jung Wang1 C.W.W. Ng2
1National
2Hong
Chiao-Tung University
Kong University of Science and Technology
Contents




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
Introduction
Constitutive Model of Compacted Soil
Numerical Analysis and Centrifuge Tests
Comparison of Calculated and
Experimental Results
Application
Conclusions
Introduction
Dynamic Stress Analysis for Earth Dam
•
•
•
Objectives
• Effective-stress modeling for earth dam
• Verification by centrifuge models
Purposes of dynamic analysis for earth dam
• to evaluate dam response under earthquake
• Stress / Acceleration
• Liquefaction Potential
• Permanent deformation/settlement
Types of analysis
• Total stress analysis
• Effective stress analysis
Effective Stress Constitutive Models
for Soil under Cyclic Loading
• Dev= f(Dg, g, No of cycles,…)
• e.g., ： Martin-Finn (1975)
• dilatancy = f( stress state, state parameters,…)
•e.g.,

Li et al. (2000)
Ueng and Lee (1990)
Du = f(damage parameters)
Du = f(k) or Dev = f (k)
•e.g.,
Finn et al.(1981) endochronic model
Park(2000) disturbed state concept
• Elasto-plastic model
•e.g.,
Manzari ＆ Dafalias (1997) , Prevost（1985）
Pastor et al, (1990), Iai et al. (2000)
Effective-stress Based
Dynamic Analysis

FEM & FDM incorporating effective stress model
appropriate for cyclic loading
e.g.,


Zienkiewicz, et al. (1981, 1984)

Beaty and Byrne (1999)

Dakoulas and Eltaher (1998)

Ming and Li (2003)
among others
Application on dynamic response of earth dam

Simulation of failure case
e.g., Lower San Fernando Dam – built by hydraulic fill
Typical Behavior of heavily compacted fill
e=10-3%
e=10-2%
e=10-1% ~1%
A Constitutive Model of Compacted Soil

Stress-strain relation
1.
2.
3.
4.
Incrementally linear
Stress-level dependent
Modulus degradation - disturbed state concept
Irrecoverable dilatancy
 Assumption
Saturated Soil
DSC ( Disturbed State Concept)
Desai and co-workers (1991)
1. Disturbance due to external loading
2. RI (Related Intact)FA (fully adjusted )
Follows a specific rule
3. Separate Constitutive laws for RI ＆ FA
 a  (1  D )   i  D   c
de a  (1  Dde )  de i  Dde  de c
Constitutive Relations
RI State :
As Dde 0
dq
de 
3G
Gmax  1000K2(max) ( 0 )0.5
p 
G  Gmax  ( )
0
i
FA State :
Seed-Idriss formula (1970)
As Dde 1
Along the failure line h=M
de c 
dq
dq

3G KM
Li and Dafalias (2000)
M
Intermediate state

For an arbitrary disturbed state

(i.e., for 1>Dde>0)
de a  (1  Dde )  de i  Dde  de c
dq
dq
de q 

 Dde
3G KM
Gt 

GKMd
KMd  3GDde
Accounting for stress history
Gt  (
GKMh
) /(1  WS )
KMh  3GDde
Ws 
 qdg
Modeling Pore Water Pressure Build-up
Irrecoverable Dilatancy
'
p
q
De vd  C  (  () tan )  ( o )  Dg
p
pa
tan  : slope of phase transformation line
C &  : material parameters
Dg : shear strain increment
D e vd : plastic volumetric strain
Pore Water Pressure Build-up
Du  De vd  Kt
Summary of Model
1.
dq
dq

 Dde
3G KMd
de a 
Progressive yielding
Dde  (
h hR 
)
M hR
 m'
G  Gmax
2.
G0  f ( m' )
3. Stress history
K 
Gt  (
M
2(1   )
G
3(1  2 )
GKMd
) /(1  WS )
KMd  3GDde
Ws 
4. Pore pressure build-up
p 
(
)
p0
 qdg
De vd

p0 
q
 C (
 ( ) tan   )  (
)  dg

p
pa
Du  De vd  Kt
Model Behavior
Stress Path
Stress-Strain
Pore Water Pressure
Build-up
Calibration of Parameters
• Parameters
Type of
parameters
Elastic
Constants
Modulus
Related
Parameters
Kmax, Gmax
β, λ , 
Dilatancy
C,ω
Critical
States
M, ψμ
• Calibration by optimization (through GA, Nonlinear)
• Objective function
 ES ij  PS ij 2

EPij  PPij 2
(
WS

WP
)

1
Best

(
)

WS

(
)

WP

ij
ij 
ij
ij 
i 1 j 1
ES
EP
i 1 j 1 

ij
ij

m
m
m
n
n
n
 (WS
i 1 j 1
ij
 WPij )  1
Centrifuge Testing

Purposes



Observation of the dynamic response of model
earth dam subjected to dynamic loadings
Verification of Numerical Model
Centrifuge tests
 Carried out in Hong Kong University of
Science and Technology
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Capacity : 400 g-tons
Arm radius : about 4.2m
Maximum centrifuge acceleration : 70g
Shaker: max. shaking acceleration 40g
Model Embankment Dam

Detail of the model embankment dam





in rectangular rigid container 712mm x 432mm x 440mm
symmetrical slopes (slope ratio 1:2)
height and base width : 190 mm and 660 mm
Leighton-Buzzard sand with Dr=90%
Carboxy methylcellulose (CMC) as the substituted pore
fluid (Dewoolkar et al 1999)
 to take time conflict of dynamic and diffusion problems
into account
 CMC is a water-soluble cellulose ether

odorless, harmless, use in food & pharmacy
Model Embankment Dam
Installed miniature sensors:
accelometers, pore pressure transducers ,
LVDTs, Laser sensors
120
Camera
120
75
Unit: mm
75
60
CMC solution
440
LVDT
Laser sensor
10
PPT7
PPT3
ACC7
ACC3
660
712
Z
46
40
ACC2 ACC4 PPT4
ACC6
50
PPT2
ACC1
PPT6
50
PPT5 ACC5
1:2
ACCb-X,Y,Z
PPT1
46
LS-h2
X
1:2
LS-h1
150
Laser sensor
ACCb1-X
Triaxial Tests

Purpose:


Calibration of parameters for the material as same
as the model embankment dam (Dr=90%)
Types of Test

Cyclic triaxial tests

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Stress controlled cyclic triaxial tests
c=0.3、0.5 、1kg/cm2
Monotonic CU tests

c= 0.3、0.5、1 kg/cm2
Dam Construction
Modeling
Static Stress Analysis
Modeling
Seepage Analysis
(obtain steady state phreatic surface)
Stress Analysis after Steady
State Seepage
(static equilibrium after steady
state seepage)
Dynamic Analysis
(in time domain)
Effective Stress Based
Numerical Analysis
120
Camera
Pore Water Pressure
120
75
CMC solution
Laser sensor
10
660
80
712
Model E2 0.13g
PPT1
PPT2
PPT7
PP(5,4)
PP(5,5)
PP(5,6)
Pore Pressure, kPa
40
20
0
0.5
1
Time, sec
1.5
2
Z
46
40
ACC2 ACC4 PPT4
ACC3
X
ACC6
PPT6
1:2
LS-h1
150
PPT2
PPT3
ACC7
50
PPT5 ACC5
PPT7
ACC1
50
46
PPT1
1:2
ACCb-X,Y,Z
0
440
LVDT
Laser sensor
LS-h2
60
Unit: mm
75
60
ACCb1-X
8
Simu
Model E2 0.13g
Input
Acceleration, g
4
Acceleration
0
-4
-8
0
0.4
0.8
1.2
1.6
2
Time, sec
12
12
Model E2 0.13g
ACC1
4
0
-4
-8
4
0
-4
-8
-12
-12
0
0.5
1
Time, sec
1.5
2
0
0.4
0.8
1.2
1.6
2
Time, sec
12
12
Model E2 0.13g
ACC2
8
Model E2 0.13g
simu ACC2
8
4
Acceleration, g
Acceleration, g
Model E2 0.13g
simu ACC(5,3)
8
Acceleration, g
Acceleration, g
8
0
-4
-8
4
0
-4
-8
-12
-12
0
0.4
0.8
1.2
Time, sec
1.6
2
0
0.4
0.8
1.2
Time, sec
1.6
2
Settlement
2
Model E2 0.13g
LVDT2
LVDT1
Ydisp(5,7)
Settlement, mm
1.5
1
0.5
0
-0.5
0
0.4
0.8
1.2
Time, sec
1.6
2
Application in Li-Yu-Tan Dam
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Li-Yu-Tan Dam
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Input motion in numerical simulation


A well instrumented earth dam.
Data was successfully recorded in Chi-Chi earthquake
Using the recorded bedrock acceleration in Chi-Chi
earthquake
Comparison of the numerical results and the
recorded data in Chi-Chi earthquake
Results of Static Analysis
Mesh
Vertical
Stress
Horizontal
Stress
Vertical
Deformation
Horizontal
Deformation
Steady-state Flow
Pore Water
Pressure
Vertical
Stress
Horizontal
Stress
Vertical
Deformation
Horizontal
Deformation
Results of Dynamic Analysis
Pore Water
Pressure
Vertical
Stress
Horizontal
Stress
Vertical
Deformation
Horizontal
Deformation
Acceleration history
in bedrock & Crest
m/sec2
sec
Comparison of Numerical Results and
Recorded Data

Maximum settlement



Horizontal deformation



Recorded settlement < 10 cm
Calculated settlement ~10cm
Downstream slope moves toward downstream,
and vice versa
Agree with the trend of instrumented data
Amplification of acceleration


About 3 times at crest
Close to the recorded data
Conclusions



Heavily compacted fill in an earth dam behaves
like a very dense soil.
An effective stress based constitutive model for
compacted fill was proposed.
This model takes into account




Progressive degradation
Stress-level dependency
Effects of stress history & Stress history
Pore water pressure build-up
Conclusions (con’d)

A numerical model for an effective stress based
analysis was



developed for dynamic analysis of earth dam
verified by the results of centrifuge tests
Effective stress analysis for a well instrumented
earth dam


using the Chi-Chi earthquake data
numerical and instrumented results were consistent
Thank you
for
Attention